BUCHI Encapsulator B-395 Pro - Manual (Page 66)

6 Operation
66 B-395 Pro Operation Manual, Version C
6 .15 Theoretical background
Equ. 1:
When a laminar jet is mechanically disturbed at the frequency ƒ,
beads of uniform size are formed
1 . The optimal wavelength λ
opt
for
breakup, according to Weber 2 is given by:
Equ. 2:
where: D = nozzle diameter
η = dynamic viscosity [Pa s]
ρ = density [kg/m 3 ]
(ca. 1000 kg/m 3 for alginate solutions)
σ = surface tension [N/m]
(ca. 55×10 -3 N/m for alginate solutions)
λ
opt
is the optimal wavelength to get the best bead formation for the given nozzle diameter and the
viscosity of the encapsulation mixture. It is possible to change λ
opt
by 30 % and still achieve a good
bead formation.
The diameter of a bead = d [m] can be calculated with the flow rate = V’ [m 3 /s] and the frequency of
the pulsation ƒaccording to:
Equ. 3:
The jet velocity = v [m/s] and the nozzle diameter = D [m] are correlated to the flow rate (V’) according
to:
Equ. 4:
Figure 6-5 shows the dependence of the flow rate to the jet velocity and the nozzle diameter as calcu-
lated by Equation 4. Because the liquid must flow laminarly the working range of the jet velocity will
normally lay between 1.5 and 2.5 m/s, depending on the liquid viscosity and the nozzle diameter.
1 Lord Rayleigh 1878. Proc. London Math. Soc. 10:4.
2 Weber C. 1936. Zeitschrift für angewandte Mathematik und Mechanik. 11:136.